2007/06/04 by Traian A. Pirvu, Pirvu, Traian A., Gordan Žitković +2
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G44 #60H30 #91B30 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #math.PR #msc:60G44 #msc:60H30 #msc:91B30 #q-fin.PM
paper · pdf · doi:10.48550/arxiv.0706.0480
arxiv created 2007/06/04 · openalex publication_date 2007/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including \em value-at-risk (VaR), \em tail-value-at-risk (TVaR), and \em limited expected loss (LEL), these constraints can be both wealth-dependent(relative) and wealth-independent (absolute). The optimal policy is shown to exist in an appropriate admissibility class, and can be obtained explicitly by uniform, state-dependent scaling down of the unconstrained (Merton) optimal portfolio. This implies that the risk-constrained wealth-growth optimizer locally behaves like a CRRA-investor, with the relative risk-aversion coefficient depending on the current values of the market coefficients.